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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 12E: Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.

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Please solve the problem abstract algebra max in 30-45 minutes thank u

1.
Let G be any group. Show that the function f: G→ G defined by f(x) = x² is group
homomorphism if and only if G is an abelian group.

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